A storyboard is a sequence of individual frames that contains illustrations that indicate key action and characters. In film making a storyboard can help to clearly define the look and feel of a scene before a camera person goes to shoot a scene (which can be VERY expensive!)
Storyboards are used for other things too, to explain the function of a device (for example a medical device), to describe a journey taken by a customer in a user experience, or to communicate the way an interface like a mobile app unfolds.
Here are a few examples:
Storyboard by designer Saul Bass for infamous shower scene from Alfred Hitchcock’s Psycho.
Here’s a video that compares the scene to the storyboard
Greg High – Marker & Prismacolor Storyboard for Heart Drug Therapy 3D Animation
A storyboard of a user experience by Steffanie Lorig. It was created in which students were asked to design an fake app that addressed issues of youth in foster care. The aim was to address the fact that kids in foster care are often disconnected from support systems when they need them most—as they exit the system. 
Storyboard of for the film Gone with the Wind
Storyboard of Taxi Driver. Drawings by Martin Scorsese.
